/sci/ - Science & Math » Thread #12703537

59KiB, 450x239, Screenshot 2021-02-14 11.22.48.png

View Same Google iqdb SauceNAO

Anonymous Sun 14 Feb 02:25:54 2021 No.12703537 View Reply Original Report

Quoted By: >>12703583 >>12703646 >>12703708 >>12703783 >>12703797 >>12704517

How do I solve this, without bothering to open the paranthesis? like, is there any substitiution possible to change it? or at least do somthing about the cubic power?

Anonymous

Anonymous Sun 14 Feb 2021 02:38:57 No.12703574 Report

Quoted By: >>12703577 >>12703603

Expand and deal with each piece as a separate integral.

Anonymous

View Same Google iqdb SauceNAO 1612766954337.png, 142KiB, 584x666

Anonymous Sun 14 Feb 2021 02:40:40 No.12703577 Report

Quoted By:

>>12703574
Thank you for doing his homework

Anonymous

Anonymous Sun 14 Feb 2021 02:42:20 No.12703583 Report

Quoted By: >>12703603

>>12703537
Use trig identities bro. sinx = 2sin(x/2) cos(x/2)

Anonymous

View Same Google iqdb SauceNAO 205.jpg, 79KiB, 600x800

Anonymous Sun 14 Feb 2021 02:43:56 No.12703587 Report

Quoted By: >>12703660

>I dont do peoples homework for them why would you think that?

Anonymous

Anonymous Sun 14 Feb 2021 02:51:15 No.12703603 Report

Quoted By: >>12703607 >>12703650

>>12703583
I tried to do so to make a ((cosx/2 + sinx/2)^2)^3, but it was a futile attempt and i have no idea what to do next

>>12703574
thats even longer than expanding it in the begining and I really want to avoid that.

Anonymous

Anonymous Sun 14 Feb 2021 02:53:24 No.12703607 Report

Quoted By: >>12703621

>>12703603
What your asking for isn't something you can really do. It's like asking how you cook a can of baked beans and stipulating that you don't want to open the can up.

Anonymous

Anonymous Sun 14 Feb 2021 02:58:26 No.12703621 Report

Quoted By: >>12703628 >>12703649

>>12703607
sometimes it's possible to solve this kind of equations using eulers identity and i was just wondering if thats the case here as well.

Anonymous

Anonymous Sun 14 Feb 2021 03:00:58 No.12703628 Report

Quoted By:

>>12703621
*integrations

Anonymous

Anonymous Sun 14 Feb 2021 03:08:22 No.12703646 Report

Quoted By: >>12703657 >>12703732

>>12703537
The easiest way is to involve branch cuts and enlist the Cauchy principal value of the integral. Once you apply the Schlaefli integral, then you use Stirling’s formula in coordination with the infinite sum representation of the trig functions (taking special care to apply residue theorem when necessary).

Anonymous

Anonymous Sun 14 Feb 2021 03:09:24 No.12703649 Report

Quoted By: >>12703657

>>12703621
Also you meant to say Euler’s formula. You can do that, but it’ll mean you have to apply the method of stationary phase.

Anonymous

Anonymous Sun 14 Feb 2021 03:10:47 No.12703650 Report

Quoted By: >>12703657 >>12703732

>>12703603
That's the right track. Now the whole integral is merely (Cos(x/2) + sin(x/2)^(6). Next use the addition identity for sine and cosine.

Anonymous

Anonymous Sun 14 Feb 2021 03:15:21 No.12703657 Report

Quoted By: >>12703678 >>12703732

>>12703650
This guy is giving you wrong answers. Do this>>12703646 or this
>>12703649
instead

Anonymous

Anonymous Sun 14 Feb 2021 03:17:00 No.12703660 Report

Quoted By: >>12703661

>>12703587
If you keep posting wojacks I will start replying to every homework thread, out of sheer spite and pettiness. I mean.. do you picture the wojack evoking a specific response from the anons you reply to? What is the intended effect, when you post them? It's alright if you tell me, this is an anonymous forum.

Anonymous

Anonymous Sun 14 Feb 2021 03:18:06 No.12703661 Report

Quoted By:

>>12703660
I post them because they have funny face

Anonymous

Anonymous Sun 14 Feb 2021 03:24:37 No.12703678 Report

Quoted By:

>>12703657
Don't confuse him. The original anon was right. Cauchy is overkill here and unnecessary

Anonymous

Anonymous Sun 14 Feb 2021 03:25:31 No.12703681 Report

Quoted By: >>12703689

>the best on my calculus class
>6 years since i last saw or did an integral
>Can't for the hell of it remember how this shit is done
Holy crap, gotta read some book to catch up. Any recommendations on books? Hopefully with exercises in it, extra internet points if it has the solutions of the exercises.

Anonymous

Anonymous Sun 14 Feb 2021 03:29:03 No.12703689 Report

Quoted By:

>>12703681
who cares about being able to solve an integral, just reach into your bag of tricks and integrate woweezowie

Anonymous

Anonymous Sun 14 Feb 2021 03:35:10 No.12703708 Report

Quoted By: >>12703783

>>12703537
you can try $\alpha = \tan x$

Anonymous

Anonymous Sun 14 Feb 2021 03:44:55 No.12703728 Report

Quoted By: >>12703774

2sin(x) + cos(x) = Acos(x + B)

Anonymous

Anonymous Sun 14 Feb 2021 03:46:08 No.12703732 Report

Quoted By:

>>12703646
thanks. it's done but i still dont really understand it. I'll have to study more

>>12703650
unfortunatly, it was not the case. you can't turn the original equation into this.

>>12703657
thanks.

Anonymous

Anonymous Sun 14 Feb 2021 04:08:07 No.12703774 Report

Quoted By:

>>12703728
took way too long for someone to suggest the obvious lmao

Anonymous

Anonymous Sun 14 Feb 2021 04:11:22 No.12703783 Report

Quoted By:

>>12703537
>>12703708
$\sin(x) = \frac{\alpha}{\pm\sqrt{\alpha^2+1}}$
$\cos(x) = \frac{1}{\pm\sqrt{\alpha^2+1}}$
$dx = (\frac{1}{\alpha^2+1})d\alpha$
then we get a bunch of integrals like
$\pm\int (2 \alpha + 1)^3 (\alpha^2+1)^{-5/2}\, d\alpha = \pm\left(\frac{14 \, \alpha^{3} - 24 \, \alpha^{2} + 3 \, \alpha - 22}{3 \, {\left(\alpha^{2} + 1\right)}^{\frac{3}{2}}}\right) + C$
$\pm\int (2 \alpha - 1)^3 (\alpha^2+1)^{-5/2}\, d\alpha = \pm\left(\frac{-14 \, \alpha^{3} - 24 \, \alpha^{2} - 3 \, \alpha - 22}{3 \, {\left(\alpha^{2} + 1\right)}^{\frac{3}{2}}}\right) + C$
stitch them up and ur good to go

Anonymous

Anonymous Sun 14 Feb 2021 04:16:37 No.12703797 Report

Quoted By:

>>12703537
This can be written as a linear combination of the first four Legendre polynomials with argument cos(x). Then the solution, using the orthonormality of the Legendre polynomials, is trivial.

Anonymous

Anonymous Sun 14 Feb 2021 10:24:54 No.12704517 Report

Quoted By:

>>12703537
.gg/TJvGnYfknX

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches